If one thinks of a Riemannian metric, $g_1$, analogously as the gradient corresponding distance function, $d_1$, with respect to background $g_0$, then natural question arises whether theory Sobolev inequalities exists between metric and its function. In this paper we study sub-critical case $p < \frac{m}{2}$ show inequality where an $L^{\frac{p}{2}}$ bound on implies $L^q$ We use result state ...

We define wt0-distance which is a special type of wt-distance and obtain some best proximity point theorems involving b-simulation functions. Our results are significant, since we replace simulation function with function, metric space b-metric space, w0-distance wt0-distance. also provide examples to support our results.

Abstract. When working with hydrological data, the ability to quantify similarity of different datasets is useful. The choice how make this quantification has a direct influence on results, measures emphasising particular sources error (for example, errors in amplitude as opposed displacements time and/or space). Wasserstein distance considers mass distributions through transport lens. In conte...

This paper introduces a novel multi-objective evolutionary algorithm based on cat swarm optimizationalgorithm (EMCSO) and its application to solve a multi-objective knapsack problem. The multi-objective optimizers try to find the closest solutions to true Pareto front (POF) where it will be achieved by finding the less-crowded non-dominated solutions. The proposed method applies cat swarm optim...