A new type of zipper fractal interpolation surfaces and associated bivariate zipper fractal operator

This note aims to introduce a bivariate fractal interpolation method by using the concept of zipper. In this note, we establish a general method to construct the zipper fractal interpolation surfaces (ZFIS) on the rectangular region. Further, the bivariate zipper fractal interpolation function (BZFIF) is used to acquire a parameterized family of (ε,α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varepsilon ,\alpha )$$\end{document}- bivariate zipper fractal function ((ε,α)-BZFF)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({(}\varepsilon {,}\alpha ){\text{-BZFF)}}$$\end{document} with respect to the prescribed zipper bivariate continuous function on the rectangular region. The bivariate zipper fractal operator (BZFO) defined in this note is bounded and linear. Several elementary aspects of this associated BZFO are reported. Further, we discuss the extension of BZFO to the Lp(J×I,B)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p} (J \times I,{\rm B})$$\end{document} spaces for 1≤p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1 \le p < \infty$$\end{document}, where B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm B}$$\end{document} is the real field ℝ or the complex field ℂ in this note.