Common Fixed-Point Theorems for Nonlinear Weakly Contractive Mappings

Chandok, Sumit; Khan, Mohammad Saeed; Abbas, Mujahid

doi:10.1007/s11253-014-0956-1

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“…It is well known that the contractive-type conditions are very indispensable in the study of fixed point theory and Banach's fixed point theorem [1] for contraction mappings is one of the pivotal results in analysis. This theorem that has been extended and generalized by various authors (see, e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15]) and has many applications in mathematics and other related disciplines as well.…”

Section: Introductionmentioning

confidence: 99%

Some fixed point theorems for (α, β)-admissible Geraghty type contractive mappings and related results

Chandok

2015

Math Sci

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In this paper, we introduced the concept of (a, b)-admissible Geraghty type contractive mappings. Sufficient conditions for the existence of a fixed point for such class of generalized nonlinear contractive mappings in metric spaces are provided. As applications, we derive a fixed point theorem for these contractions whenever the space is endowed with a graph. Some interesting consequences of our theorems are also obtained. The proved results generalize and extend various well-known results in the literature. Some examples are illustrated for the usability of the results.

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