This paper addresses the non-linear programming problem of globally minimizing the real valued function x⟶d(x,Sx) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event...

The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x → d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm...

Let us suppose that A and B are nonempty subsets of a metric space. Let S:A⟶B and T:A⟶B be nonself-mappings. Considering the fact S and T are nonself-mappings, it is feasible that the equations Sx=x and Tx=x have no common solution, designated as a common fixed point of the mappings S and T....

Given non-empty subsets A and B of a metric space, let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S{:}A{\longrightarrow} B}$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${T {:}A{\longrightarrow} B}$$</EquationSource> </InlineEquation> be non-self mappings. Due to the fact that S and T are non-self mappings, the equations Sx=x and Tx=x are likely to have no common solution, known as a common fixed point...</equationsource></inlineequation></equationsource></inlineequation>