New extension of some fixed point results in complete metric spaces

Debnath, Pradip; Neog, Murchana; Radenović, Stojan

doi:10.1515/tmj-2017-0037

Cited by 2 publications

(1 citation statement)

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“…There have been enormous developments in the area of existence and uniqueness of fixed point for multi valued and set valued mappings in various directions-see [5][6][7][8][9][10][11][12][13][14][15][16]. Some references that have been instrumental for the current work are [17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction

2019

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The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

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