Some results on multi-valued weakly jungck mappings in b-metric space

Abstract

In this paper, the concept of multi-valued weak contraction of Berinde and Berinde [8] for the Picard iteration in a complete metric space is extended to the case of multi-valued weak contraction for the Jungck iteration in a complete b-metric space. While our main results generalize the recent results of Berinde and Berinde [8], they also extend, improve and unify several classical results pertainning to single and multi-valued contractive mappings in the fixed point theory. Our results also improve the recent results of Daffer and Kaneko [16].

Common fixed point theorems for non-compatible self-maps in b-metric spaces

“…Since then, several papers deal with fixed point theory for single-valued and multivalued operators in b−metric spaces (see also [2,4,5,6,7,8,9,10,11,14,16,19,21,24]). Pacurar [21] proved results on sequences of almost contractions and fixed points in b−metric spaces.…”

Some Fixed Point Theorems for pair mapping in Complex Valued b-Metric Space

“…so that (38) This implies that which proves the uniqueness of common fixed point in . This completes the proof of the theorem.…”

“…Using this idea researcher presented generalization of the renowned Banach Fixed Point Theorem in the b-metric space for ( [27], [28][29]). Many authers have studied the extension of Fixed Point Theorem in b-metric space, see for instance ([30], [31,32,33], [34], [35], [36], [37] [38], [39], [40,41][42] [43], [44], [45]& [46]& [47]). In 1978, Feisher and khan [9] generalized the Banach Contraction Principle with rational expression and proved some fixed and common fixed point theorems.…”

Resolving systems of nonlinear integral equations via C-class functions

“…In Czerwik (1993) and Czerwik (1998) extended many results related to the bmetric spaces. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric spaces (Akkouchi, 2011;Aydi et al, 2012;Boriceanu, 2009;Boriceanu et al, 2010;Bota et al, 2011;Hussain & Shah, 2011;Olatinwo, 2008;Huang et al, 2015;Mustafa et al, 2013;Mustafa et al, 2014;Ansari et al, 2014;Aghajani et al, 2014).…”