GENERALIZED WARDOWSKI TYPE FIXED POINT THEOREMS VIA α-ADMISSIBLE FG-CONTRACTIONS IN b-METRIC SPACES

doi:10.1016/S0252-9602(16)30080-7

Abstract

Abstract:

Recently, Wardowski [Fixed Point Theory Appl., 2012:94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. In this paper, we introduce an α-β-FG-contraction and generalize the Wardowski fixed point result in b-metric and ordered b-metric spaces. As an application of our results we deduce Suzuki type fixed point results for β-FG-contractions. Moreover, we discuss some illustrative examples to highlight the realized improvements.

Key words: α-admissible mapping, F-contraction, α-continuous function

CLC Number:

47H10

Vahid PARVANEH, Nawab HUSSAIN, Zoran KADELBURG. GENERALIZED WARDOWSKI TYPE FIXED POINT THEOREMS VIA α-ADMISSIBLE FG-CONTRACTIONS IN b-METRIC SPACES[J].Acta mathematica scientia,Series B, 2016, 36(5): 1445-1456.

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References

[1] Wardowski D. Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl, 2012, 2012:94
[2] Abbas M, Ali B, Romaguera S. Fixed and periodic points of generalized contractions in metric spaces. Fixed Point Theory Appl, 2013, 2013:243
[3] Wardowski D, Van Dung N. Fixed points of F-weak contractions on complete metric spaces. Demonstratio Math, 2014, 47(1):146-155
[4] Piri H, Kumam P. Some fixed point theorems concerning F-contraction in complete metric spaces. Fixed Point Theory Appl, 2014, 2014:210
[5] Samet B, Vetro C, Vetro P. Fixed point theorem for α-ψ-contractive type mappings. Nonlinear Anal, 2012, 75:2154-2165
[6] Hussain N, Kutbi M A, Salimi P. Fixed point theory in α-complete metric spaces with applications. Abstract Appl Anal, 2014, 2014:280817
[7] Karap?nar K, Kumam P, Salimi P. On α-ψ-Meir-Keeler contractive mappings. Fixed Point Theory Appl, 2013, 2013:94
[8] Salimi P, Latif A, Hussain H. Modified α-ψ-contractive mappings with applications. Fixed Point Theory Appl, 2013, 2013:151
[9] Hussain H, Salimi P, Latif A. Fixed point results for single and set-valued α-η-ψ-contractive mappings. Fixed Point Theory Appl, 2013, 2013:212
[10] Bakhtin I A. The contraction principle in quasimetric spaces[in Russian]. Funk An Ulianowsk Gos Ped Inst, 1989, 30:26-37
[11] Czerwik S. Contraction mappings in b-metric spaces. Acta Math Inf Univ Ostrav, 1993, 1:5-11
[12] Czerwik S. Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem Mat Fis Univ Modena, 1998, 46:263-276
[13] Khamsi M A, Hussain N. KKM mappings in metric type spaces. Nonlinear Anal, 2010, 73(9):3123-3129
[14] Jovanovi? M, Kadelburg Z, Radenovi? S. Common fixed point results in metric-type spaces. Abstr Appl Anal, 2010, 2010:978121
[15] Boriceanu M, Bota M, Petrusel A. Multivalued fractals in b-metric spaces. Cent Eur J Math, 2010, 8(2):367-377
[16] Hussain N,-Dori? D, Kadelburg Z, Radenovi? S. Suzuki-type fixed point results in metric type spaces. Fixed Point Theory Appl, 2012, 2012:126
[17] Hussain N, Parvaneh V, Roshan J R, Kadelburg Z. Fixed points of cyclic (ψ, φ, L, A, B)-contractive mappings in ordered b-metric spaces with applications. Fixed Point Theory Appl, 2013, 2013:256
[18] Roshan J R, Parvaneh V, Sedghi S, Shobkolaei N, Shatanawi W. Common fixed points of almost generalized (ψ, φ)_s-contractive mappings in ordered b-metric spaces. Fixed Point Theory Appl, 2013, 2013:159
[19] Aghajani A, Abbas M, Roshan J R. Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces. Math Slovaca, 2014, 64(4):941-960
[20] Ran A C M, Reurings M C B. A fixed point theorem in partially ordered sets and some application to matrix equations. Proc Amer Math Soc, 2004, 132:1435-1443
[21] Nieto J J, Rodr?guez-Lopez R. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order, 2005, 22:223-239
[22] Suzuki T. A generalized Banach contraction principle that characterizes metric completeness. Proc Amer Math Soc, 2008, 136:1861-1869
[23] Suzuki T. A new type of fixed point theorem in metric spaces. Nonlinear Anal, 2009, 71(11):5313-5317
[24] Hussain N, Salimi P. Suzuki-Wardowski type fixed point theorems for α-GF-contractions. Taiwan J Math, 2014, 18(6):1879-1895