Abstract:In this paper we present some absolute retract results for modified Geraghty multivalued type contractions in b-metric space. Our results, generalize several existing results in the corresponding literature. We also present some examples to support the obtained results. c 2016 all rights reserved.
“…2 Department of Mathematics, Çankaya University, 06790, Ankara, Etimesgut, Turkey. 3 Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia.…”
In this work, new theorems and results related to fixed point theory are presented. The results obtained are used for the sake of proving the existence and uniqueness of a positive solution of a coupled system of equations that involves fractional derivatives in the Riemann–Liouville settings and is subject to boundary conditions in the form of integrals.
“…2 Department of Mathematics, Çankaya University, 06790, Ankara, Etimesgut, Turkey. 3 Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586, Riyadh, Saudi Arabia.…”
In this work, new theorems and results related to fixed point theory are presented. The results obtained are used for the sake of proving the existence and uniqueness of a positive solution of a coupled system of equations that involves fractional derivatives in the Riemann–Liouville settings and is subject to boundary conditions in the form of integrals.
“…This notion became popular and raised interest among researchers after the paper of Huang and X. Zhang [1] in 2007. Since then, a number of authors got the characterization of several known fixed point theorems in the context of Banach-valued metric space, such as, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”
In this manuscript, we investigate the existence and uniqueness of a common fixed point for the self-mappings defined on quasi-cone metric space over a divisible Banach algebra via an auxiliary mapping ϕ.
“…Following this success, many authors have continued to work on this trend and reported several improvements, advances in the setting of b-metric spaces, see e.g. [5][6][7][8][9][10][11][12].…”
The aim of this paper is to investigate the interpolative contractions involving rational forms in the framework of b-metric spaces. We prove the existence of a fixed point of such a mapping with different combinations of the rational forms. A certain example is considered to indicate the validity of the observed result.
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