000117144 001__ 117144 000117144 005__ 20240319080953.0 000117144 0247_ $$2doi$$a10.3390/math10010011 000117144 0248_ $$2sideral$$a128203 000117144 037__ $$aART-2022-128203 000117144 041__ $$aeng 000117144 100__ $$0(orcid)0000-0003-4847-0493$$aNavascues, Maria A.$$uUniversidad de Zaragoza 000117144 245__ $$aBinary operations in metric spaces satisfying side inequalities 000117144 260__ $$c2022 000117144 5060_ $$aAccess copy available to the general public$$fUnrestricted 000117144 5203_ $$aThe theory of metric spaces is a convenient and very powerful way of examining the behavior of numerous mathematical models. In a previous paper, a new operation between functions on a compact real interval called fractal convolution has been introduced. The construction was done in the framework of iterated function systems and fractal theory. In this article we extract the main features of this association, and consider binary operations in metric spaces satisfying properties as idempotency and inequalities related to the distance between operated elements with the same right or left factor (side inequalities). Important examples are the logical disjunction and conjunction in the set of integers modulo 2 and the union of compact sets, besides the aforementioned fractal convolution. The operations described are called in the present paper convolutions of two elements of a metric space E. We deduce several properties of these associations, coming from the considered initial conditions. Thereafter, we define self-operators (maps) on E by using the convolution with a fixed component. When E is a Banach or Hilbert space, we add some hypotheses inspired in the fractal convolution of maps, and construct in this way convolved Schauder and Riesz bases, Bessel sequences and frames for the space. 000117144 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000117144 590__ $$a2.4$$b2022 000117144 592__ $$a0.446$$b2022 000117144 591__ $$aMATHEMATICS$$b23 / 329 = 0.07$$c2022$$dQ1$$eT1 000117144 593__ $$aComputer Science (miscellaneous)$$c2022$$dQ2 000117144 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2 000117144 593__ $$aEngineering (miscellaneous)$$c2022$$dQ2 000117144 594__ $$a3.5$$b2022 000117144 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000117144 700__ $$aRajan, Pasupathi 000117144 700__ $$aChand, Arya Kumar Bedabrata 000117144 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000117144 773__ $$g10, 1 (2022), 11 [17 pp.]$$pMathematics (Basel)$$tMathematics$$x2227-7390 000117144 8564_ $$s866612$$uhttps://zaguan.unizar.es/record/117144/files/texto_completo.pdf$$yVersión publicada 000117144 8564_ $$s2694372$$uhttps://zaguan.unizar.es/record/117144/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000117144 909CO $$ooai:zaguan.unizar.es:117144$$particulos$$pdriver 000117144 951__ $$a2024-03-18-13:18:19 000117144 980__ $$aARTICLE