c65197bf13c99742aad9d26c4feb3082 Sym_a2022v14n11p2247.pdf 0bf988c1134b1843db02fa8f5785e856697f4e67 Sym_a2022v14n11p2247.pdf f71a47055f744aa1c0172fba2576134ca9ecc828b1f3a594e80b7c432589d828 Sym_a2022v14n11p2247.pdf Title: Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points Subject: This paper studies a general p -contractive condition of a self-mapping T on X , where ( X ,d ) is either a metric space or a dislocated metric space, which combines the contribution to the upper-bound of d( Tx,Ty ) , where x and y are arbitrary elements in X of a weighted combination of the distances d( x,y ) ,d( x,Tx ),d( y,Ty ),d( x,Ty ),d( y,Tx ) , | d( x,Tx ) - d( y,Ty ) | and | d( x,Ty ) - d( y,Tx ) | . The asymptotic regularity of the self-mapping T on X and the convergence of Cauchy sequences to a unique fixed point are also discussed if ( X,d ) is complete. Subsequently, ( T, S ) generalized cyclic p -contraction pairs are discussed on a pair of non-empty, in general, disjoint subsets of X . The proposed contraction involves a combination of several distances associated with the ( T, S ) -pair. Some properties demonstrated are: (a) the asymptotic convergence of the relevant sequences to best proximity points of both sets is proved; (b) the best proximity points are unique if the involved subsets are closed and convex, the metric is norm induced, or the metric space is a uniformly convex Banach space. It can be pointed out that both metric and a metric-like (or dislocated metric) possess the symmetry property since their respective distance values for any given pair of elements of the corresponding space are identical after exchanging the roles of both elements. Keywords: p-contraction; p-contraction pair; best proximity points; uniformly convex Banach space Author: Manuel De la Sen and Asier Ibeas Creator: LaTeX with hyperref Producer: xdvipdfmx (20200315) CreationDate: Thu Nov 10 06:23:09 2022 CET ModDate: Thu Nov 10 06:36:37 2022 CET Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 28 Encrypted: no Page size: 595.28 x 841.89 pts (A4) Page rot: 0 File size: 6451271 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- EVRDZX+PalatinoLinotype-Bold CID TrueType Identity-H yes yes yes 9 0 RSAWEJ+CMR10 Type 1C Builtin yes yes yes 16 0 JAPZGZ+CMSY10 Type 1C Builtin yes yes yes 21 0 QIEXSM+PalatinoLinotype-Roman CID TrueType Identity-H yes yes yes 26 0 QTOHRY+PalatinoLinotype-Italic CID TrueType Identity-H yes yes yes 33 0 SOZTAU+PalatinoLinotype-BoldItalic CID TrueType Identity-H yes yes yes 40 0 YDXIRC+VNR8 Type 1C Builtin yes yes yes 47 0 LSFLPE+URWPalladioL-Roma Type 1C WinAnsi yes yes yes 52 0 OCKZHQ+URWPalladioL-Ital Type 1C WinAnsi yes yes yes 57 0 GXBWHU+TimesNewRomanPS-BoldMT Type 1C WinAnsi yes yes no 77 0 CSRIGL+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 80 0 YFPCLC+CMMI10 Type 1C Builtin yes yes yes 106 0 QFVVDJ+PazoMath Type 1C Builtin yes yes yes 114 0 SIYXYH+PazoMath-Italic Type 1C Builtin yes yes yes 119 0 QOQDSI+CMEX10 Type 1C Builtin yes yes no 127 0 KYXRTT+MSAM10 Type 1C Builtin yes yes yes 137 0 DMBGAI+Calibri CID TrueType Identity-H yes yes yes 221 0 DMBGAI+Calibri CID TrueType Identity-H yes yes yes 235 0 QAVNDD+VNR9 Type 1C Builtin yes yes yes 247 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2023-12-14 02:34:21 CET RepresentationInformation: Sym_a2022v14n11p2247.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2023-12-13 18:04:43 CET Size: 6451271 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 404 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: 0 Item: Title: Main Asymptotic Regularity and Fixed Point Results for a Class of Generalized p-Contractions in Metric Spaces and in Dislocated Metric Spaces Destination: 1 Item: Title: Some Convergence and Best Proximity Results for a Class of Generalized (T, S) Cyclic p-Contraction Pairs in Metric Spaces Destination: 2 Item: Title: Numerical Examples Destination: 3 Children: Item: Title: Fixed Points for Generalized p-Contractive Mappings Destination: 4 Item: Title: Fixed Points for Generalized ( T,S ) Cyclic p-Contractive Mappings Destination: 5 Item: Title: Concluding Remarks Destination: 6 Item: Title: References Destination: 6 Info: Title: Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points Author: Manuel De la Sen and Asier Ibeas Subject: This paper studies a general p -contractive condition of a self-mapping T on X , where ( X ,d ) is either a metric space or a dislocated metric space, which combines the contribution to the upper-bound of d( Tx,Ty ) , where x and y are arbitrary elements in X of a weighted combination of the distances d( x,y ) ,d( x,Tx ),d( y,Ty ),d( x,Ty ),d( y,Tx ) , | d( x,Tx ) - d( y,Ty ) | and | d( x,Ty ) - d( y,Tx ) | . The asymptotic regularity of the self-mapping T on X and the convergence of Cauchy sequences to a unique fixed point are also discussed if ( X,d ) is complete. Subsequently, ( T, S ) generalized cyclic p -contraction pairs are discussed on a pair of non-empty, in general, disjoint subsets of X . The proposed contraction involves a combination of several distances associated with the ( T, S ) -pair. Some properties demonstrated are: (a) the asymptotic convergence of the relevant sequences to best proximity points of both sets is proved; (b) the best proximity points are unique if the involved subsets are closed and convex, the metric is norm induced, or the metric space is a uniformly convex Banach space. It can be pointed out that both metric and a metric-like (or dislocated metric) possess the symmetry property since their respective distance values for any given pair of elements of the corresponding space are identical after exchanging the roles of both elements. Keywords: p-contraction; p-contraction pair; best proximity points; uniformly convex Banach space Creator: LaTeX with hyperref Producer: xdvipdfmx (20200315) CreationDate: Thu Nov 10 06:23:09 CET 2022 ModDate: Thu Nov 10 06:36:37 CET 2022 ID: 0xef6adb486e84971f74afaeef374ef10f, 0xef6adb486e84971f74afaeef374ef10f Filters: FilterPipeline: FlateDecode Fonts: Type0: Font: BaseFont: QTOHRY+PalatinoLinotype-Italic Encoding: Identity-H ToUnicode: true Font: BaseFont: SOZTAU+PalatinoLinotype-BoldItalic Encoding: Identity-H ToUnicode: true Font: BaseFont: EVRDZX+PalatinoLinotype-Bold Encoding: Identity-H ToUnicode: true Font: BaseFont: QIEXSM+PalatinoLinotype-Roman Encoding: Identity-H ToUnicode: true Type1: Font: BaseFont: RSAWEJ+CMR10 FontSubset: true FirstChar: 40 LastChar: 93 FontDescriptor: FontName: RSAWEJ+CMR10 Flags: Serif, Symbolic FontBBox: -40, -250, 1009, 750 FontFile3: true ToUnicode: true Font: BaseFont: QFVVDJ+PazoMath FontSubset: true FirstChar: 68 LastChar: 229 FontDescriptor: FontName: QFVVDJ+PazoMath Flags: Serif, Symbolic FontBBox: -40, -283, 878, 946 FontFile3: true ToUnicode: true Font: BaseFont: LSFLPE+URWPalladioL-Roma FontSubset: true FirstChar: 44 LastChar: 59 FontDescriptor: FontName: LSFLPE+URWPalladioL-Roma Flags: Serif, Symbolic FontBBox: -166, -283, 1021, 943 FontFile3: true Encoding: WinAnsiEncoding ToUnicode: true Font: BaseFont: JAPZGZ+CMSY10 FontSubset: true FirstChar: 0 LastChar: 112 FontDescriptor: FontName: JAPZGZ+CMSY10 Flags: Serif, Symbolic, Italic FontBBox: -29, -960, 1116, 775 FontFile3: true ToUnicode: true Font: BaseFont: SIYXYH+PazoMath-Italic FontSubset: true FirstChar: 35 LastChar: 122 FontDescriptor: FontName: SIYXYH+PazoMath-Italic Flags: Serif, Symbolic, Italic FontBBox: -70, -277, 902, 733 FontFile3: true ToUnicode: true Font: BaseFont: QAVNDD+VNR9 FontSubset: true FirstChar: 189 LastChar: 189 FontDescriptor: FontName: QAVNDD+VNR9 Flags: Serif, Symbolic FontBBox: -39, -250, 1036, 750 FontFile3: true ToUnicode: true Font: BaseFont: OCKZHQ+URWPalladioL-Ital FontSubset: true FirstChar: 65 LastChar: 122 FontDescriptor: FontName: OCKZHQ+URWPalladioL-Ital Flags: Serif, Symbolic, Italic FontBBox: -170, -305, 1010, 941 FontFile3: true Encoding: WinAnsiEncoding ToUnicode: true Font: BaseFont: KYXRTT+MSAM10 FontSubset: true FirstChar: 3 LastChar: 3 FontDescriptor: FontName: KYXRTT+MSAM10 Flags: Serif, Symbolic FontBBox: 8, -463, 1331, 1003 FontFile3: true ToUnicode: true Font: BaseFont: YFPCLC+CMMI10 FontSubset: true FirstChar: 60 LastChar: 62 FontDescriptor: FontName: YFPCLC+CMMI10 Flags: Serif, Symbolic, Italic FontBBox: -32, -250, 1048, 750 FontFile3: true ToUnicode: true Font: BaseFont: YDXIRC+VNR8 FontSubset: true FirstChar: 225 LastChar: 225 FontDescriptor: FontName: YDXIRC+VNR8 Flags: Serif, Symbolic FontBBox: -36, -250, 1070, 750 FontFile3: true ToUnicode: true Font: BaseFont: QOQDSI+CMEX10 FontSubset: true FirstChar: 0 LastChar: 125 FontDescriptor: FontName: QOQDSI+CMEX10 Flags: Serif, Symbolic FontBBox: -24, -2960, 1454, 772 FontFile3: true CIDFontType2: Font: BaseFont: QTOHRY+PalatinoLinotype-Italic CIDSystemInfo: Registry: Adobe Registry: Identity Supplement: 0 FontDescriptor: FontName: QTOHRY+PalatinoLinotype-Italic Flags: Serif, Symbolic, Italic FontBBox: -162, -291, 1249, 1052 FontFile2: true Font: BaseFont: SOZTAU+PalatinoLinotype-BoldItalic CIDSystemInfo: Registry: Adobe Registry: Identity Supplement: 0 FontDescriptor: FontName: SOZTAU+PalatinoLinotype-BoldItalic Flags: Serif, Symbolic, Italic, ForceBold FontBBox: -156, -291, 1305, 1050 FontFile2: true Font: BaseFont: EVRDZX+PalatinoLinotype-Bold CIDSystemInfo: Registry: Adobe Registry: Identity Supplement: 0 FontDescriptor: FontName: EVRDZX+PalatinoLinotype-Bold Flags: Serif, Symbolic, ForceBold FontBBox: -174, -299, 1445, 1050 FontFile2: true Font: BaseFont: QIEXSM+PalatinoLinotype-Roman CIDSystemInfo: Registry: Adobe Registry: Identity Supplement: 0 FontDescriptor: FontName: QIEXSM+PalatinoLinotype-Roman Flags: Serif, Symbolic FontBBox: -170, -292, 1419, 1050 FontFile2: true Pages: Page: Sequence: 1 Annotations: Annotation: Subtype: Link Rect: 114, 348, 136, 355 Annotation: Subtype: Link Rect: 35, 336, 125, 343 Annotation: Subtype: Link Rect: 35, 167, 155, 209 Annotation: Subtype: Link Rect: 130, 91, 151, 98 Annotation: Subtype: Link Rect: 35, 79, 140, 86 Annotation: Subtype: Link Rect: 35, 757, 259, 811 Annotation: Subtype: Link Rect: 514, 757, 602, 815 Annotation: Subtype: Link Rect: 130, 647, 139, 656 Annotation: Subtype: Link Rect: 220, 647, 229, 656 Annotation: Subtype: Link Rect: 230, 262, 235, 273 ActionDest: 244 Annotation: Subtype: Link Rect: 488, 116, 493, 126 ActionDest: 244 Annotation: Subtype: Link Rect: 123, 18, 251, 27 Annotation: Subtype: Link Rect: 410, 18, 559, 27 Annotation: Subtype: Link Rect: 35, 423, 143, 459 Page: Sequence: 2 Annotations: Annotation: Subtype: Link Rect: 316, 646, 321, 656 ActionDest: 244 Annotation: Subtype: Link Rect: 217, 608, 221, 618 ActionDest: 244 Annotation: Subtype: Link Rect: 224, 608, 229, 618 ActionDest: 244 Annotation: Subtype: Link Rect: 384, 596, 389, 606 ActionDest: 244 Annotation: Subtype: Link Rect: 392, 596, 397, 606 ActionDest: 244 Annotation: Subtype: Link Rect: 422, 596, 427, 606 ActionDest: 244 Annotation: Subtype: Link Rect: 394, 583, 399, 593 ActionDest: 244 Annotation: Subtype: Link Rect: 518, 558, 523, 568 ActionDest: 244 Annotation: Subtype: Link Rect: 333, 533, 343, 543 ActionDest: 244 Annotation: Subtype: Link Rect: 284, 520, 294, 530 ActionDest: 244 Annotation: Subtype: Link Rect: 379, 520, 389, 530 ActionDest: 244 Annotation: Subtype: Link Rect: 498, 470, 508, 480 ActionDest: 244 Annotation: Subtype: Link Rect: 512, 395, 522, 405 ActionDest: 244 Annotation: Subtype: Link Rect: 527, 395, 537, 405 ActionDest: 244 Annotation: Subtype: Link Rect: 298, 73, 308, 83 ActionDest: 244 Page: Sequence: 3 Annotations: Annotation: Subtype: Link Rect: 231, 671, 236, 681 ActionDest: 244 Annotation: Subtype: Link Rect: 238, 671, 243, 681 ActionDest: 244 Annotation: Subtype: Link Rect: 231, 609, 236, 619 ActionDest: 244 Annotation: Subtype: Link Rect: 287, 501, 292, 511 ActionDest: 244 Annotation: Subtype: Link Rect: 456, 476, 461, 486 ActionDest: 244 Annotation: Subtype: Link Rect: 245, 375, 255, 386 ActionDest: 244 Page: Sequence: 4 Page: Sequence: 5 Page: Sequence: 6 Annotations: Annotation: Subtype: Link Rect: 295, 461, 300, 471 ActionDest: 244 Annotation: Subtype: Link Rect: 550, 461, 555, 471 ActionDest: 244 Annotation: Subtype: Link Rect: 262, 399, 267, 409 ActionDest: 244 Annotation: Subtype: Link Rect: 269, 399, 274, 409 ActionDest: 244 Annotation: Subtype: Link Rect: 367, 386, 377, 396 ActionDest: 244 Page: Sequence: 7 Page: Sequence: 8 Annotations: Annotation: Subtype: Link Rect: 246, 394, 250, 404 ActionDest: 244 Page: Sequence: 9 Page: Sequence: 10 Page: Sequence: 11 Annotations: Annotation: Subtype: Link Rect: 401, 550, 406, 560 ActionDest: 244 Page: Sequence: 12 Page: Sequence: 13 Page: Sequence: 14 Page: Sequence: 15 Annotations: Annotation: Subtype: Link Rect: 454, 650, 459, 660 ActionDest: 244 Annotation: Subtype: Link Rect: 455, 458, 460, 468 ActionDest: 244 Page: Sequence: 16 Annotations: Annotation: Subtype: Link Rect: 525, 674, 530, 684 ActionDest: 244 Annotation: Subtype: Link Rect: 533, 674, 543, 684 ActionDest: 244 Annotation: Subtype: Link Rect: 393, 661, 398, 672 ActionDest: 244 Annotation: Subtype: Link Rect: 309, 611, 314, 621 ActionDest: 244 Annotation: Subtype: Link Rect: 452, 611, 462, 621 ActionDest: 244 Annotation: Subtype: Link Rect: 461, 574, 471, 584 ActionDest: 244 Annotation: Subtype: Link Rect: 313, 524, 323, 534 ActionDest: 244 Annotation: Subtype: Link Rect: 180, 486, 190, 496 ActionDest: 252 Page: Sequence: 17 Page: Sequence: 18 Annotations: Annotation: Subtype: Link Rect: 441, 91, 446, 101 ActionDest: 179 Annotation: Subtype: Link Rect: 418, 66, 423, 76 ActionDest: 179 Page: Sequence: 19 Annotations: Annotation: Subtype: Link Rect: 489, 721, 494, 731 ActionDest: 179 Annotation: Subtype: Link Rect: 518, 696, 523, 706 ActionDest: 179 Annotation: Subtype: Link Rect: 211, 126, 216, 136 ActionDest: 5 Annotation: Subtype: Link Rect: 222, 126, 227, 136 ActionDest: 244 Annotation: Subtype: Link Rect: 278, 126, 283, 136 ActionDest: 184 Page: Sequence: 20 Annotations: Annotation: Subtype: Link Rect: 376, 270, 380, 279 ActionDest: 5 Annotation: Subtype: Link Rect: 386, 270, 391, 279 ActionDest: 244 Annotation: Subtype: Link Rect: 388, 197, 393, 207 ActionDest: 189 Annotation: Subtype: Link Rect: 438, 172, 443, 182 ActionDest: 189 Annotation: Subtype: Link Rect: 294, 147, 299, 157 ActionDest: 195 Annotation: Subtype: Link Rect: 326, 134, 331, 144 ActionDest: 189 Page: Sequence: 21 Annotations: Annotation: Subtype: Link Rect: 241, 160, 246, 170 ActionDest: 195 Page: Sequence: 22 Annotations: Annotation: Subtype: Link Rect: 287, 285, 292, 295 ActionDest: 195 Annotation: Subtype: Link Rect: 329, 164, 334, 174 ActionDest: 202 Page: Sequence: 23 Annotations: Annotation: Subtype: Link Rect: 367, 493, 377, 503 ActionDest: 252 Annotation: Subtype: Link Rect: 445, 126, 455, 136 ActionDest: 252 Page: Sequence: 24 Annotations: Annotation: Subtype: Link Rect: 459, 684, 471, 694 ActionDest: 176 Annotation: Subtype: Link Rect: 198, 633, 203, 643 ActionDest: 207 Annotation: Subtype: Link Rect: 435, 621, 440, 631 ActionDest: 207 Annotation: Subtype: Link Rect: 251, 596, 256, 606 ActionDest: 207 Page: Sequence: 25 Annotations: Annotation: Subtype: Link Rect: 409, 709, 414, 719 ActionDest: 214 Annotation: Subtype: Link Rect: 269, 462, 274, 473 ActionDest: 230 Annotation: Subtype: Link Rect: 290, 450, 295, 460 ActionDest: 244 Annotation: Subtype: Link Rect: 198, 437, 203, 448 ActionDest: 230 Page: Sequence: 26 Annotations: Annotation: Subtype: Link Rect: 302, 276, 306, 285 ActionDest: 244 Page: Sequence: 27 Annotations: Annotation: Subtype: Link Rect: 280, 522, 315, 531 Annotation: Subtype: Link Rect: 60, 499, 95, 508 Annotation: Subtype: Link Rect: 114, 475, 150, 485 Annotation: Subtype: Link Rect: 198, 452, 234, 462 Annotation: Subtype: Link Rect: 489, 441, 524, 450 Annotation: Subtype: Link Rect: 303, 418, 339, 427 Annotation: Subtype: Link Rect: 229, 395, 265, 404 Annotation: Subtype: Link Rect: 277, 372, 313, 381 Annotation: Subtype: Link Rect: 182, 349, 218, 358 Annotation: Subtype: Link Rect: 183, 326, 218, 335 Annotation: Subtype: Link Rect: 110, 291, 145, 300 Annotation: Subtype: Link Rect: 520, 280, 556, 289 Annotation: Subtype: Link Rect: 357, 257, 392, 266 Annotation: Subtype: Link Rect: 352, 234, 387, 243 Annotation: Subtype: Link Rect: 60, 211, 95, 220 Annotation: Subtype: Link Rect: 105, 188, 141, 197 Annotation: Subtype: Link Rect: 218, 165, 254, 174 Annotation: Subtype: Link Rect: 105, 142, 141, 151 Annotation: Subtype: Link Rect: 416, 130, 451, 139 Annotation: Subtype: Link Rect: 225, 84, 261, 93 Page: Sequence: 28 Annotations: Annotation: Subtype: Link Rect: 307, 699, 343, 709 Annotation: Subtype: Link Rect: 470, 676, 505, 686 Checksum: 9d6e8d5a Type: CRC32 Checksum: c65197bf13c99742aad9d26c4feb3082 Type: MD5 Checksum: 0bf988c1134b1843db02fa8f5785e856697f4e67 Type: SHA-1 Checksum: f71a47055f744aa1c0172fba2576134ca9ecc828b1f3a594e80b7c432589d828 Type: SHA-256