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Based on the translates of a fractal multiquadric function defined on a grid, we propose two fractal quasi-interpolants <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_C^{\\alpha }f$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msubsup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mi>C<\/mml:mi>\n                      <mml:mi>\u03b1<\/mml:mi>\n                    <\/mml:msubsup>\n                    <mml:mi>f<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_D^{\\alpha }f$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msubsup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mi>D<\/mml:mi>\n                      <mml:mi>\u03b1<\/mml:mi>\n                    <\/mml:msubsup>\n                    <mml:mi>f<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to approximate smooth and irregular functions. We study the convergence of <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_C^{\\alpha }f$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msubsup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mi>C<\/mml:mi>\n                      <mml:mi>\u03b1<\/mml:mi>\n                    <\/mml:msubsup>\n                    <mml:mi>f<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_D^{\\alpha }f$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:msubsup>\n                      <mml:mi>L<\/mml:mi>\n                      <mml:mi>D<\/mml:mi>\n                      <mml:mi>\u03b1<\/mml:mi>\n                    <\/mml:msubsup>\n                    <mml:mi>f<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to <jats:italic>f<\/jats:italic> using uniform error estimates. We investigate the linear polynomial reproducing property, convexity\/concavity and monotonicity features of these quasi-interpolation operators. The advantages of fractal quasi-interpolants over the classical quasi-interpolants are demonstrated by various examples.<\/jats:p>","DOI":"10.1007\/s40314-024-02802-7","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T11:01:46Z","timestamp":1718362906000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Shape preserving fractal multiquadric quasi-interpolation"],"prefix":"10.1007","volume":"43","author":[{"given":"D.","family":"Kumar","sequence":"first","affiliation":[]},{"given":"A. K. B.","family":"Chand","sequence":"additional","affiliation":[]},{"given":"P. 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