The increasing significance of theorem proving-based formalization in mathematics and computer science highlights the necessity for formalizing foundational mathematical theories. In this work, we employ Coq interactive prover to methodically formalize language, semantics, syntax propositional logic, a fundamental aspect reasoning proof construction. We construct four Hilbert-style axiom system...

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

Abstract We present the generalized optical theorem and its applications with special emphasis on roles of bound states. First, we prove which gives a necessary sufficient condition for function $\langle {\bf {\it k}^{\prime}} | T k}} \rangle$ two variables $\ k}}^{\prime }$ ${\bf k}}$ to be physically acceptable as half-on-shell T-matrix, i.e., have an underlying Hermitian potential V. Second,...