On Pointwise Lacunary Statistical Convergence of Order α of Sequences of Function

In this paper we introduce the concepts of pointwise lacunary statistical convergence of order α and pointwise wp(f,θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_{p}(f,\theta )$$\end{document}—summability of order α of sequences of real valued functions. Also some relations between pointwise Sθα(f)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\theta }^{\alpha }(f)$$\end{document}—statistical convergence and pointwise wpα(f,θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_{p}^{\alpha }(f,\theta )$$\end{document}—summability are given.