We prove non-archimedean analogue of Sendov’s conjecure. also provide complete list polynomials over an algebraically closed field $$K$$ that satisfy the optimal bound in conjecture.

An action for a prospect of $p$-adic open superstring on target Minkowski space is proposed. The constructed `worldsheet' fields taking values in the field $\mathbb{Q}_p$, but it assumed to be obtained from discrete Bruhat-Tits tree. This proven have an analog worldsheet supersymmetry and superspace also terms superfields. does not conformal symmetry, however implemented definition amplitudes. ...

in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article.

For more than two millennia, ever since Euclid’s geometry, the so called Archimedean Axiom has been accepted without sufficiently explicit awareness of that fact. The effect has been a severe restriction of our views of space-time, a restriction which above all affects Physics. Here it is argued that, ever since the invention of Calculus by Newton, we may actually have empirical evidence that t...

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential for...

Jointly with H.-P. Künzi we started investigating a concept of spherical completeness in ultra-quasipseudometric spaces which we called q-spherical completeness. In this article we study fixed point theorems in a space X endowed with a non-Archimedean asymmetric norm structure. Here we extend certain results of Petalas and Vidalis and Kirk and Shahzad.