SOME TOPOLOGICAL PROPERTIES OF A GENERALIZED S-METRIC SPACE TOGETHER WITH SOME FIXED POINT RESULTS AND THEIR APPLICATIONS

SOME TOPOLOGICAL PROPERTIES OF A GENERALIZED S-METRIC SPACE TOGETHER WITH SOME FIXED POINT RESULTS AND THEIR APPLICATIONS

K. Roy

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Abstract

In this paper, the concept of S(p,q) b -metric space is introduced as a generalization of S-metric space, Sb-metric space, (p, q)-metric space and QM(n, b)-metric space. A topology is formed with the help of S(p,q) b -metric and some topological properties are studied to establish Cantor’s intersection theorem. Sehgal-Guseman, Reich and Akram type fixed point theorems are proved over such spaces. Several examples are given in support of our results. Moreover, the proven fixed point theorems are applied to well-posedness and Ulam-Hyers stability of fixed point problems.

Keywords

Fixed point, S(p,q) b -metric space, Ulam-Hyers stability and well-posedness of fixed point problems