Abstract
In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.
Highlights
With a view to enhance the domain of applicability, Matthews [1] initiated the idea of a partial metric space by weakening the metric conditions and proved an analogue of Banach contraction principle in such spaces
Thereafter, many well-known results of metric fixed point theory were extended to partial metric spaces
Alam and Imdad [21] extended the Banach contraction principle to complete metric space endowed with an arbitrary binary relation
Summary
With a view to enhance the domain of applicability, Matthews [1] initiated the idea of a partial metric space by weakening the metric conditions and proved an analogue of Banach contraction principle in such spaces. Thereafter, many well-known results of metric fixed point theory were extended to partial metric spaces (see [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and references therein). Alam and Imdad [21] extended the Banach contraction principle to complete metric space endowed with an arbitrary binary relation. This idea has inspired intense activity in this theme, and there exists considerable literature around this result (e.g., [6,21,22,23,24,25]). Several well-known contraction conditions such as Kannan type, Chatterjee type, Ciric type, phi-contractions, and some others were introduced in this direction
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