Bv(s)-Fixed Point Theorem In Metric Space

The purpose of this thesis is to study the fixed point problems of Pata-type contractive mapping and Khan-type contractive mapping of C-class functions in _vb(s)-metric space.The convergence and boundedness of sequences in space are obtained by adding appropriate conditions,thus the fixed point theorem is proved.The research results of this paper are new,and the existing research results at home and abroad have been further promoted and unified.In this text:First,some basic concepts,background and significance of the topic are introduced.The related concepts and applications of fixed point problems are reviewed,and the results of previous studies on contractive mapping and fixed point problems are summarized.Based on this,the main contents of this paper are proposed.Secondly,the preparatory knowledge needed in this paper is given to provide theoretical basis and support for the subsequent proof.Thirdly,under the condition of Pata-type compression,the fixed point theorem on _vb(s)-metric space is obtained,and the Pata-type common fixed point results of two mappings in _vb(s)-metric space are established.Then,the sufficient conditions for the existence of C-class functions on the generalized contractive Khan-type maps with rational expressions are obtained.An example is given to support the results.The results in the literature are further generalized and unified by that in this paper.Finally,the summary is given,and the problems worthy of further research and exploration are brought out.