000060399 001__ 60399 000060399 005__ 20170217164309.0 000060399 0248_ $$2sideral$$a97928 000060399 037__ $$aART-2016-97928 000060399 041__ $$aeng 000060399 100__ $$aKatiyar, Saurabh 000060399 245__ $$aHidden-variable alpha-fractal functions and their monotonicity aspects. 000060399 260__ $$c2016 000060399 5060_ $$aAccess copy available to the general public$$fUnrestricted 000060399 5203_ $$aFractal interpolation that possesses the ability to produce smooth and nonsmooth inter- polants is a novice to the subject of interpolation. Apart from appropriate degree of smooth- ness, a good interpolant should reflect shape properties, for instance monotonicity, inherent in a prescribed data set. Despite the flexibility offered by these shape preserving fractal interpolants developed recently in the literature are well-suited only for the representation of self-referential functions. In this article we present hidden variable A-fractal interpo- lation function as a tool to associate an entire family of R2-valued continuous functions f[A] parameterized by a suitable block matrix A with a prescribed function f ¿ C(I,R2). Depending on the choice of parameters, the members of the family may be self-referential, or non-self-referential, and preserve some properties of original function f, thus yielding more diversity and flexibility in the process of approximation. As an application of the developed theory, we introduce a new class of monotone C1-cubic interpolants by taking full advantage of flexibility offered by the hidden variable A-fractal interpolation functions (HFIFs). This theory invoked to the C1-cubic spline HFIF, which can be viewed as a fractal perturbation of the traditional C1-cubic spline, culminates with the desired monotonicity preserving C1-cubic HFIF. The monotonicity preserving interpolation scheme developed herein generalizes and enriches its traditional nonrecursive counterpart and its fractal ex- tension. 000060399 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc$$uhttp://creativecommons.org/licenses/by-nc/3.0/es/ 000060399 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000060399 700__ $$aChand, A.K. Bedabrata 000060399 700__ $$0(orcid)0000-0003-4847-0493$$aNavascués Sanagustín, María Antonia$$uUniversidad de Zaragoza 000060399 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDepartamento de Matemática Aplicada$$cMatemática Aplicada 000060399 773__ $$g71 (2016), 7-30$$pRev. Acad. Cienc. Exactas, Fís.-Quím. Nat. Zaragoza$$tRevista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza$$x0370-3207 000060399 8564_ $$s576095$$uhttps://zaguan.unizar.es/record/60399/files/texto_completo.pdf$$yVersión publicada 000060399 8564_ $$s86198$$uhttps://zaguan.unizar.es/record/60399/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000060399 909CO $$ooai:zaguan.unizar.es:60399$$particulos$$pdriver 000060399 951__ $$a2017-02-17-11:08:12 000060399 980__ $$aARTICLE